Aluminum alloy castings are widely used in the automotive industry to reduce weight and improve fuel efficiency. To improve mechanical properties, the aluminum castings are usually subject to a full T6/T7 heat treatment, which includes a solution treatment at a relatively high temperature, quenching in a cold medium such as water, and then age hardening at an intermediate temperature. A significant amount of residual stresses can be developed in aluminum castings when they are quenched, particularly in water. Li, P., Maijer, D. M., Lindley, T. C., 2007, “Simulating the Residual Stress in An A356 Automotive Wheel and its Impact on Fatigue Life,” Metallurgical and Materials Transactions B, 38(4) pp. 505-515; Li, K., Xiao, B., and Wang, Q., 2009, “Residual Stresses in As-Quenched Aluminum Castings,” SAE International Journal of Materials & Manufacturing, 1(1) pp. 725-731. The existence of residual stresses, in particular tensile residual stresses, can have a significant detrimental influence on the performance of a structural component. In many cases, the high tensile residual stresses can also result in a severe distortion of the component, and they can even cause cracking during quenching or subsequent manufacturing processes. Li, P., Maijer, D. M., Lindley, T. C., 2007, “Simulating the Residual Stress in An A356 Automotive Wheel and Its Impact on Fatigue Life,” Metallurgical and Materials Transactions B, 38(4) pp. 505-515; Lee, Y. L., Pan, J., Hathaway, R., 2005, “Fatigue Testing and Analysis: Theory and Practice,” Elsevier Butterworth-Heinemann, pp. 402.
The amount of residual stresses and distortion produced in cast aluminum components during quenching depends significantly on the quenching rate and the extent of non-uniformity of the temperature distribution in the casting during quenching. The heat transfer of aluminum castings during quenching involves conduction, convection, radiation, and even phase transformation, depending upon quenching medium. In a water quenching process, the heat transfer of the aluminum castings involves at least three main stages including film boiling (1), nucleate boiling (2), and convection (3), as illustrated in FIG. 1. Holman, J. P., 2002, “Heat Transfer,” McGraw-Hill, N.Y., pp. 665.
Each of these stages has very different characteristics. The first stage of cooling is characterized by the formation of a vapor film (steam) around the component. This is a period of relatively slow cooling during which heat transfer occurs by radiation and conduction through the vapor (steam) blanket. With the increase in the thickness of the vapor (steam) film, however, the stable steam film eventually collapses, and water comes into contact with the hot metal surface, resulting in nucleate boiling and a high heat extraction rate. With the continuous boiling, the metal surface temperature decreases rapidly to a point at which boiling ceases and heat is removed by convection into the water. As a result, heat is removed very slowing during this stage.
FIG. 2 illustrates a general relationship between the heat transfer rate a and the temperature difference ΔT (the quench process proceeds in the direction of the arrow (from right to left). When the hot metal surface contacts the water at the beginning of quenching, the ΔT is so high that the generation of steam becomes too fast, and most of the metal surface is covered by the steam bubbles (film boiling (1)). As a result, there is no more water in direct contact with the metal surface to be agitated. Therefore, a negative effect takes place (because of the low α of steam, the heat-transfer rate is 1/20 that of water), and it becomes a matter of heat transfer between the metal surface and the steam mainly through conduction. A relatively slow cooling continues with the increase of the thickness of the steam blanket and the decrease of ΔT, as illustrated in FIG. 2. When α and q decrease to a point at a in the α−ΔT curve (FIG. 2), the stable steam film eventually collapses, and water comes into contact directly with the hot casting surface resulting in nucleate boiling (2) and a quick increase of the heat extraction rate (between a to b in α-ΔT curve in FIG. 2). At this stage, the water is fully agitated by the generated steam bubbles. The maximum heat transfer qmax is reached at point b in the α−ΔT curve by the combined effect of the increased a and the decreased ΔT. After point b, the boiling continues but becomes mild, and the metal surface temperature decreases rapidly. As a result, the agitation and the heat transfer rate a decrease dramatically following b-c in the α−ΔT curve in FIG. 2. When the casting surface temperature decreases to certain point, the boiling ceases, and heat is removed by convection (3) into the water. In this case, the heat transfer rate α is lower.
Because the boiling phenomenon is so complicated, theoretical analysis of the boiling heat transfer has long been a challenging problem, even with the state-of-the-art sophisticated computational fluid dynamics (CFD) algorithm. Although a relational function of α or q on ΔT is as presented in FIG. 2, where a and b are the points for the minimum and maximum values of q, the abc part of the curve (as will be discussed later) is so unstable that it is hard to obtain in practice.
Film Boiling
Film boiling can be treated as single phase wall problem. Nukiyama, S., 1984, “The Maximum and Minimum Values of the Heat Q Transmitted from Metal to Boiling Water Under Atmospheric Pressure,” International Journal of Heat and Mass Transfer, 27(7) pp. 959-970. The heat transfer during film boiling is simply described as:q=α(ΔT)(Tmetal>about 500° C.)  (1)where q is the heat transmitted from the casting surface per unit area per unit time to the water; α is the heat-transfer coefficient, and ΔT is the temperature difference between the casting surface and the water, as illustrated in FIG. 3. For cast aluminum components solution-treated at 540° C. and then quenched in water (<100° C.), the film boiling takes place at relatively high temperature (>500° C.).Nucleate Boiling
The heat transfer during nucleate boiling can be calculated based on an empirical equation:q=c1(ΔT)c2(Tmetal<about 500° C.)  (2)where c1 and c2 are constants that can be calibrated with the material and quench conditions, as illustrated in FIG. 3. Rohsenow, W. 1952, “A method of correlating heat transfer data for surface boiling of liquids”, Trans. ASME vol. 74, 969-976.
Because of the complexity of phase transformation, and in particular bubble nucleation and interaction, accurate modeling of heat transfer of cast aluminum alloys in water quenching remains a significant challenge.
There are many classical empirical equations reported in the literature for calculating heat transfer and interface heat transfer coefficients. However, their applications are very limited because almost all of them are calibrated under certain specific experimental conditions which can be significantly different from the actual production situation. In recent years, CFD simulations of fluid flow and heat transfer have made significant progress. But, the current CFD prediction of heat transfer and temperature distribution of aluminum castings during water quenching is not accurate because the complicated interaction and heat transfer phenomena between water and hot aluminum castings are not fully understood and represented in the state-of-the-art fluid flow and heat transfer code. FIGS. 4A-B show examples of the significant discrepancy observed in the thermal simulation using a state-of-the-art fluid flow and heat transfer code in comparison with experimental measurements.
To precisely predict the amount of residual stresses and distortion induced in cast aluminum components during quenching as well as the mechanical properties and durability of the quenched cast aluminum components during service, it is vital to understand the heat transfer and calculate accurate temperature distributions in the casting during quenching. Therefore, there is a need to develop improved methods and systems that can accurately predict the heat transfer and temperature distributions in the cast aluminum components during water quenching.